Mathematics
Grade9
Easy

Question

Find the value of x.

  1. 14
  2. 42
  3. 7
  4. 6

hintHint:

the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.

The correct answer is: 7


    fraction numerator 3 x minus 1 over denominator 24 end fraction equals fraction numerator 2 x plus 1 over denominator 18 end fraction left parenthesis A n g l e space b i s e c t o r space t h e o r e m right parenthesis
18 left parenthesis 3 x minus 1 right parenthesis equals 24 left parenthesis 2 x plus 1 right parenthesis
54 x minus 18 equals 48 x plus 24
54 x minus 48 x equals 24 plus 18
6 x equals 42
fraction numerator X equals 42 over denominator 6 equals 7 end fraction
    Hence, the correct option is D.

    The base is divided in the same ratio as the sides of the angle.

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